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Application of magnetics for geothermal exploration
Geothermal energy is the natural heat of the Earth. The thinned and fractured crust
allows the magma to rise to the surface as lava. The greatest part of the magma does not reach
the surface but heats large regions of underground rocks. Rainwater can seep down the faults
and fractured rocks for miles. After being heated, it can return to the surface as steam or hot
water. When hot water and steam reach the surface, they can form fumaroles, hot springs,
mud pots and other interesting phenomena. Otherwise, when the rising hot water and steam is
trapped in permeable and porous rocks under a layer of impermeable rock, it can form a
geothermal reservoir, which could be a powerful source of energy. This clean renewable
energy can be used in many areas having accessible geothermal resources. For finding them
geological, geochemical and geophysical surveys are necessary to be done. Magnetic can be
an important part of the complex of geophysical geothermal exploration methods.
As is known, crustal rocks lose their magnetization at the Curie point temperature. At
this temperature, ferromagnetic rocks become paramagnetic, and their ability to generate
detectable magnetic anomalies disappears. The Curie temperature for titanomagnetite, the
most common magnetic mineral in igneous rocks, is less than approximately 570OC. It has
been established that an increase in titanium content of titanomagnetite causes a reduction in
Curie temperature and the titanium content generally increases in the more mafic igneous
rocks (Byerly and Stolt, 1977). Consequently, it may be possible to locate a point on the
isothermal surface by determining the depth to the bottom of a polarized rock mass. Thus the
deepest level in the crust containing materials which create discernible signatures in a
magnetic anomaly map is generally interpreted as the depth to the Curie isotherm.
One of the important parameters which determine the relative depth of the isotherm
with respect to sea level is the heat content in a particular region. The heat content is
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generally proportional to the local temperature gradient, thermal capacity, and generation of
heat. A region with significant geothermal energy near the surface of the earth is
characterized by an anomalously high temperature gradient and heat flow. It is therefore to be
expected that regardless of the composition of the rocks, the region will be associated with a
conspicuously shallow Curie point isotherm relating to the adjoining regions isotherm
(Bhattacharyya and Leu, 1977).
Magnetic anomalies are analyzed for estimating the depths to the bottoms of
magnetized bodies in the crust. These depths, when contoured for the entire area, should
provide a picture of the spatial variation of the Curie isotherm level. This picture should
correlate to a significantly high degree with various known indices of geothermal activity in
the area under consideration. The practical importance of a study on this correlation lies in the
possibility of establishing a useful reconnaissance method, based on geomagnetic data, for
rapid, regional geothermal exploration.
The method has been very popular during the last 30 years. Many projects have been
made for reconfirmation of prospective geothermal areas, analysis of regional relationships
among known geothermal areas, and discovery of new geothermal prospects using the
creation of a Curie point depth map as an integral part of the exploration (Yellowstone
National Park, Cascade Range of Oregon, Japanese Islands, Northern Red Sea, Trans-
Mexican Volcanic Belt, parts of Greece, etc.).
The mathematical model on which the great mass of the analysis is based is a
collection of random samples from a uniform distribution of rectangular prisms, each having a
constant magnetization. The model was introduced by Spector and Grant (1970), and has
proven very successful in estimating average depths to the tops of magnetized bodies. One
principal result of their analysis is that the expectation value of the spectrum for the model is
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the same as that of a single body with the average parameters for the collection. In polar
coordinates ( )s, in frequency space, this spectrum has the form ( ) ( )[ ]F s JA N i L M, cos sin = + +2
( )[ ] + +n i l mcos sin
( ) ( ) sin coscos
sin sinsin
sasa
sbsb
(1)
( )( ) +exp cos sin2 0 0 is x y ( ) ( )[ ] exp exp2 2 sz szt b , where
J magnetization per unit volume;
A average cross-sectional area of the bodies;
L, M, N direction cosines of geomagnetic field;
l, m, n direction cosines of the average magnetization vector;
a, b average body x- and y- dimensions;
xo , yo average body x- and y- centre location;
zt , zb average depths to the top and bottom of the bodies;
Following Bhattacharyya and Leu (1975, 1977), Okubo et al. (1985) approach the
estimation of bottom depths in two steps: first, find the centroid depth zo; and second,
determine the depth to the top zt . The depth to the bottom (inferred Curie point depth) is
calculated from these values: zb= 2zo- zt . This method recognizes that there is no wavelength
range in which the exponential signal from the bottom dominates the one from the top and
that a direct calculation of depth to the bottom requires a simultaneous computation of the
depth to the top a much more complex problem. The terms involving zt and zb can be recast
into a hyperbolic sine function of zt and zb plus a centroid term. At very long wavelengths
(compared to the body dimensions), the hyperbolic sine tends to unity, leaving a single term
containing z0, the centroid. The terms involving the body parameters (a, b, zb - zt) may be
approximated by their leading terms, to yield:
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( ) ( )[ ]F s VJs N i L M, cos sin = + +4 2 ( )[ ] + +n i l mcos sin ( )( ) +exp cos sin2 0 0 is x y (2) ( ) exp 2 0sz , where V is the average body volume
Equation (2) can be recognized as the spectrum of a dipole. In effect, the ensemble
average at these very low frequencies is that of a random distribution of point dipoles. A few
methods were found for estimating z0 from equation (2) (Bhattacharya and Leu, 1975, Spector
and Grant, 1970). The most important finding is that the following decision will be
independent of the details of the body parameters (prism, cylinders, or whatever), provided
that the dimensions in all directions are comparable. Since geothermal areas are often in
volcanic regions and are likely to have strong remanent magnetization, the second advantage
of the algorithm is that there was not invoked reduction to the pole, or even assumption for
induced magnetization was made. Numerical experiments have shown that there were not
significant differences between results obtained with and without reduction.
At somewhat shorter wavelengths, the signal from the top dominates the spectrum
and an estimate of the depth to the top can be obtained. Returning to equation (1) and
assuming that a range of wavelengths can be found for which the following approximations
hold:
( )sin cos
cos
sa
sa 1,
( )sin sin
sin
sb
sb 1,
and ( )exp 2 0szb
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the spectrum reduces to the form
( ) ( )[ ]F s JA N i L M, cos sin = + +2 ( )[ ] + +n i l mcos sin (3) ( )( ) +exp cos sin2 0 0 is x y ( ) exp 2szt .
To make sense for the above approximations, the bodies must in general be large in depth
compared to their horizontal dimensions. Equation (3) is in fact the spectrum of a monopole.
Because of the similarities to equation (2) the same methods to estimating zt can be used.
With the averaged location of the centroid and the mean depth to the tops of magnetized
bodies known, it is simple and straightforward to calculate the mean depth to the bottoms of
these bodies. The calculated depth is interpreted as the depth to the Curie isotherm for the
block. Then taking into account the average elevation of the ground surface and assuming the
value of the Curie point temperature the temperature gradient in depth can be estimated.
Similar studies have shown a strong correlation between geothermal hot regions and
the thickness of the magnetized crust.
REFERENCES
Bhattacharyya, B. K., and Leu, L. K., 1975a, Spectral analysis of gravity and magnetic
anomalies due to two-dimensional structures: Geophysics, 40, 993-1013.
Bhattacharyya, B. K., and Leu, L. K., 1975b, Analysis of magnetic anomalies over
Yellowstone National Park: Mapping of Curie point isothermal surface for geothermal
reconnaissance: J. Geophys. Res., 80, 4461-4465.
Bhattacharyya, B. K., and Leu, L. K., 1977, Spectral analysis of gravity and magnetic
anomalies due to rectangular prismatic bodies: Geophysics, 42, 41-50.
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Byerly, P. E., and Stolt, R. H., 1977, Attempt to define the Curie point isotherm in Northern
and Central Arizona: Geophysics, 42, 1394-1400.
Campos-Enriquez, J. O., Arroyo-Esquivel, M. A., and Urrutia-Fucugauchi, J., 1990,
Basement, Curie isotherm and shallow-crustal structure of the Trans-Mexican Volcanic
Belt, from aeromagnetic data: Tectonophysics, 172, 77-90.
Connard, G., Couch, R., and Gemperie, M., 1983, Analysis of aeromagnetic measurements
from the Cascade Range in central Oregon: Geophysics, 48, 376-390.
Nemzer, M. L., Carter, A. K., Nemzer, K. P., 2004, Geothermal energy facts: Geothermal
Education Office, on-line at: http:// geothermal.marin.org/pwrheat.html.
Okubo, Y., Graff, R. G., Hansen, R. O., Ogawa, K., Tsu, H., 1985, Curie point depths of the
Island of Kyushu and surrounding areas : Geophysics, 53, 481-494.
Okubo, Y., Matsushima, J., Correia, A., 2003, Magnetic spectral analysis in Portugal and its
adjasent seas: Physics and Chemistry of the Earth, 28, 511-519.
Salem, A., Ushijima, K., Elsirafi, A., and Mizunaga, H., 2000, Spectral analysis of
aeromagnetic data for geothermal recconnaissance of Quseir area, Northern Red Sea,
Egypt: Proceedings World Geothermal Congress, 1669-1673, on-line at :
http://www.geotermie.de/egec-geothernet/ci-prof/africa/egypt/0221.pdf
Spector, A. and Grant, F. S., 1970, Statistical models for interpreting aeromagnetic data :
Geophysics, 35, 293-302.
Stampolidis, A. and Tsokas, G., 2002, Curie point depths of Macedonia and Thrace, N.
Greece : Pure and Applied Geophysics, 159, 1-13.